We need to calculate a z-score to determine the probability of getting a month with a temperature of 34 degrees or higher, and then subtract that probability from 1 to get the final result.
Explanation:To solve this problem, we're dealing with a normal distribution. The average maximum monthly temperature in Campinas, Brazil is given as the mean (29.9 degrees). The standard deviation has been given as 2.31 degrees.
We're asked to find the percentage of months that would have a maximum temperature of 34 degrees or higher. This can be interpreted as finding the probability of a temperature being more than 34 degrees. We first need to find the number of standard deviations away from the mean 34 degrees is, which is known as Z-score.
The formula for Z-score is (X - mean) / standard deviation. So, our calculation would be (34 - 29.9) / 2.31. The resultant Z-score would have to be looked up in a standard normal distribution table, which will give us the probability up to that point. As we want the probability of the temperature being higher, we'll subtract the value we get from 1 (as total probability is 1), which would give us the percentage of months with a maximum temperature of 34 degrees or higher.
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The population of a certain species of fish has a growth rate of 2.2% per year. It is estimated that the the current population is 350,000. Estimate the number of years it will take the fish population to reach 1,000,000. Round your answer to the nearest tenth.
We have been given that the population of a certain species of fish has a growth rate of 2.2% per year. It is estimated that the the current population is 350,000.
We are asked to find the time it will take the fish population to reach 1,000,000.
We will use exponential growth formula to solve our given problem.
An exponential growth function is in form [tex]y=a\cdot (1+r)^x[/tex], where,
y = Final amount,
a = Initial amount,
r = Growth rate in decimal form,
x = Time
[tex]2.2\%=\frac{2.2}{100}=0.022[/tex]
[tex]y=350,000\cdot (1+0.022)^x[/tex]
To find the time for the fish population to reach 1,000,000, we will substitute [tex]x=1,000,000[/tex] in our equation as:
[tex]1,000,000=350,000\cdot (1+0.022)^x[/tex]
[tex]1,000,000=350,000\cdot (1.022)^x[/tex]
[tex]\frac{1,000,000}{350,000}=\frac{350,000\cdot (1.022)^x}{350,000}[/tex]
[tex]2.8571428571428571=(1.022)^x[/tex]
Now we will take natural log on both sides:
[tex]\text{ln}(2.8571428571428571)=\text{ln}((1.022)^x)[/tex]
[tex]\text{ln}(2.8571428571428571)=x\cdot \text{ln}(1.022)[/tex]
[tex]x=\frac{\text{ln}(2.8571428571428571)}{\text{ln}(1.022)}[/tex]
[tex]x=\frac{1.0498221244986776733}{0.0217614917815127}[/tex]
[tex]x=48.2421947[/tex]
Upon rounding to nearest tenth, we will get:
[tex]x\approx 48.2[/tex]
Therefore, it will take approximately 48.2 years for the fish population to reach 1,000,000.
Answer:
47.7
Step-by-step explanation:
right answer
Write an equation in slope intercept form for $750 and $600 and $1150
Answer:
y = 0.5x + 10
Step-by-step explanation:
Step 1 :
Identify the independent and dependent variables.
The independent variable (x) is the square footage of floor space.
The dependent variable (y) is the monthly rent.
Step 2 :
Write the information given in the problem as ordered pairs.
The rent for 600 square feet of floor space is $750 :
(600, 750)
The rent for 900 square feet of floor space is $1150 :
(900, 1150)
Step 3 :
Find the slope.
m = (y₂ - y₁) / (x₂ - x₁)
Substitute (600, 750) for (x₁, y₁) and (900, 1150) for (x₂, y₂).
m = (1150 - 750) / (900 - 600)
m = 400 / 300
m = 4/3
Step 4 :
Find the y-intercept.
Use the slope 4/3 and one of the ordered pairs (600, 750).
Slope-intercept form :
y = mx + b
Plug m = 4/3, x = 600 and y = 750.
750 = (4/3)(600) + b
750 = (4)(200) + b
750 = 800 + b
-50 = b
Step 5 :
Substitute the slope and y-intercept.
Slope-intercept form
y = mx + b
Plug m = 4/3 and b = -50
y = (4/3)x + (-50)
y = (4/3)x - 50
Problem 2 :
Hari’s weekly allowance varies depending on the number of chores he does. He received $16 in allowance the week he did 12 chores, and $14 in allowance the week he did 8 chores. Write an equation for his allowance in slope-intercept form.
Solution :
Step 1 :
Identify the independent and dependent variables.
The independent variable (x) is number of chores Hari does per week
The dependent variable (y) is the allowance he receives per week.
Step 2 :
Write the information given in the problem as ordered pairs.
For 12 chores, he receives $16 allowance :
(12, 16)
For 8 chores, he receives $14 allowance :
(8, 14)
Step 3 :
Find the slope.
m = (y₂ - y₁) / (x₂ - x₁)
Substitute (12, 16) for (x₁, y₁) and (8, 14) for (x₂, y₂).
m = (14 - 16) / (8 - 12)
m = (-2) / (-4)
m = 1/2
m = 0.5
Step 4 :
Find the y-intercept.
Use the slope 0.5 and one of the ordered pairs (8, 14).
Slope-intercept form :
y = mx + b
Plug m = 0.5, x = 8 and y = 14.
14 = (0.5)(8) + b
14 = 4 + b
10 = b
Step 5 :
Substitute the slope and y-intercept.
Slope-intercept form
y = mx + b
Plug m = 0.5 and b = 10
y = 0.5x + 10
Scientists measure how much water and debris flows past a river station at different time of the year. The water and debris are called discharge. the table show the average discharge at a research station on a certain river in 2 months. How many more quarts of discharge per second are there in march than February? How many quarts of discharge per second were recorded in march and February. There are blank more quarts per second in march and February
Answer:
2664
Step-by-step explanation:
(2285gallons - 1619gallons) =
666 gallons * 4quarts(in a gallon) =
2664 Quarts
A study was conducted to measure the effectiveness of a diet program that claims to help manage weight. Subjects were randomly selected to participate. Before beginning the program, each participant was given a score based on his or her fitness level. After six months of following the diet, each participant received another score. The study wanted to test whether there was a difference between before and after scores. What is the correct alternative hypothesis for this analysis?
a. μ≠0
b. μd≠0
c. p1≠p2
Answer:
x=test value before , y = test value after
The system of hypothesis for this case are:
Null hypothesis: [tex]\mu_y- \mu_x = 0[/tex]
Alternative hypothesis: [tex]\mu_y -\mu_x \neq 0[/tex]
If we define the difference as [tex] d = y_i-x_i[/tex] we convert the system of hypothesis:
Null hypothesis: [tex]\mu_d = 0[/tex]
Alternative hypothesis: [tex]\mu_d \neq 0[/tex]
Step-by-step explanation:
Previous concepts
A paired t-test is used to compare two population means where you have two samples in which observations in one sample can be paired with observations in the other sample. For example if we have Before-and-after observations (This problem) we can use it.
Let put some notation
x=test value before , y = test value after
The system of hypothesis for this case are:
Null hypothesis: [tex]\mu_y- \mu_x = 0[/tex]
Alternative hypothesis: [tex]\mu_y -\mu_x \neq 0[/tex]
If we define the difference as [tex] d = y_i-x_i[/tex] we convert the system of hypothesis:
Null hypothesis: [tex]\mu_d = 0[/tex]
Alternative hypothesis: [tex]\mu_d \neq 0[/tex]
An operation manager at an electronics company wants to test their amplifiers. The design engineer claims they have a mean output of 364364 watts with a standard deviation of 1212 watts. What is the probability that the mean amplifier output would be greater than 364.8364.8 watts in a sample of 5252 amplifiers if the claim is true? Round your answer to four decimal places.
Answer:
The probability that the mean amplifier output would be greater than 364.8 watts in a sample of 52 amplifiers is 0.3156
Step-by-step explanation:
Mean output of amplifiers = 364
Standard deviation = [tex]\sigma[/tex] = 12
We have to find the probability that the mean output for 52 randomly selected amplifiers will be greater than 364.8. Since the population is Normally Distributed and we know the value of population standard deviation, we will use the z-distribution to solve this problem.
We will convert 364.8 to its equivalent z-score and then finding the desired probability from the z-table. The formula to calculate the z-score is:
[tex]z=\frac{x-\mu}{\frac{\sigma}{\sqrt{n} } }[/tex]
x=364.8 converted to z score for a sample size of n= 52 will be:
[tex]z=\frac{364.8-364}{\frac{12}{\sqrt{52} } }=0.48[/tex]
This means, the probability that the output is greater than 364.8 is equivalent to probability of z score being greater than 0.48.
i.e.
P( X > 364.8 ) = P( z > 0.48 )
From the z-table:
P( z > 0.48) = 1 - P(z < 0.48)
= 1 - 0.6844
= 0.3156
Since, P( X > 364.8 ) = P( z > 0.48 ), we can conclude that:
The probability that the mean amplifier output would be greater than 364.8 watts in a sample of 52 amplifiers is 0.3156
Alton High School sold adult and student tickets for a school play. Of the 128 tickets sold, 84 were student tickets. What percent of the total tickets sold, rounded to the nearest percent, were adult tickets?
Answer:
66%Step-by-step explanation:
84/128=.65625
.65625x100=65.625=66%
Final answer:
To calculate the percentage of adult tickets sold for the school play, subtract the student tickets from the total tickets sold to find the number of adult tickets (44), and then divide by the total number of tickets and multiply by 100 to get the percentage, which is approximately 34%.
Explanation:
The question asks us to find what percent of the total tickets sold at a school play were adult tickets. Alton High School sold a total of 128 tickets, of which 84 were student tickets. To calculate the number of adult tickets, we subtract the number of student tickets from the total number of tickets: 128 - 84 = 44 adult tickets.
Next, we calculate the percent of adult tickets out of the total tickets sold by using the formula:
Percent = (Number of adult tickets / Total number of tickets) imes 100
Plugging in our numbers, we get:
Percent = (44 / 128) imes 100
Percent = 0.34375 imes 100
Percent ≈ 34%
Rounded to the nearest percent, we find that approximately 34% of the tickets sold were for adults.
Which statement correctly compares the ratios?
The ratio 9 to 12 is greater than 4 to 6.
The ratio 9 to 12 is less than 4 to 6.
O The ratio 9 to 12 is equal to 4 to 6.
The ratios cannot be compared.
HIERE
Answer:
its 9 to 12 is greater than 4 to 6.
Step-by-step explanation:
As per the given question, the correct option is the ratio 9 to 12 is greater than 4 to 6.
Explanation:In comparing the ratios 9 to 12 and 4 to 6, we first need to simplify both ratios. The ratio 9 to 12 can be simplified by dividing both numbers by their greatest common divisor, which is 3. This gives us a simplified ratio of 3 to 4.
Similarly, the ratio 4 to 6 can be simplified by dividing both numbers by their greatest common divisor, which is 2, giving us a simplified ratio of 2 to 3.
If we convert both ratios to decimals by dividing the first number by the second in each pair, we'll find that 9/12 = 0.75 and 4/6 = 0.67, which shows that the first ratio is greater. Therefore, we find that the correct statement is the ratio 9 to 12 is greater than 4 to 6.
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How many 9s are there in 63?
.
Answer:
7
Step-by-step explanation:
63 ÷ 9 = 7
5x+9=24 solve the equation
Answer:
x=3
Step-by-step explanation:
24-9
15/5
3
x=3
Answer:
x = 3
Step-by-step explanation:
3 * 5 + 9 =24
What is a difference of squares that has a factor of x+8?
Answer:
x^2 - 64
Step-by-step explanation:
A difference of squares is a special product in the form (a^2 - b^2)..their factored form is (a - b)(a + b)..
Thus here a = x and b = 8, thus if x + 8 is a factor, then x - 8 is also a factor..
(x + 8)(x - 8) <-- expand this out using difference of squares rules..
= (x)^2 - (8)^2
= x^2 - 64 <-- answer...
You could also expand that using FOIL (FOIL - first, outer, inner, last)..
(x + 8)(x - 8)
= (x)(x) + (x)(-8) + (8)(x) + (8)(-8)
= x^2 - 8x + 8x - 64 <-- the -8x and 8x cancels out..leaving you with..
= x^2 - 64
The difference of squares that has a factor of x+8 is x² - 64.
What is Algebraic Identity?An algebraic identity is an equality that holds for any values of its variables.
For example, the identity ( x + y )² = x² + 2xy + y²
(x+y)² = x² + 2xy + y²
(x+y)²=x²+2xy+y² holds for all values of x and y.
As, Difference of two squares
x² - y² = (x - y)(x + 8)
So, for difference of squares that has (x -8) as one of the factor.
The other factor is (x + 8)
So, we can write
(x - 8)(x + 8) = x² - 8²
= x² - 64.
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Jason is entering a weight
lifting contest. Currently, his
maximum bench press weight is
105 pounds. If he increases the
weight by 7 pounds each week,
What is the maximum weight
he be able to bench press
after 13 weeks?
Answer:
196
Step-by-step explanation:
7 x 13 = 91 + 105
Find the area of a sector of a circle whose radius is 7 cm and whose central angle is 45
degrees. Use pi = 3.14.
Answer:
The area of a sector of a circle = 19.2325
Step-by-step explanation:
Explanation:-
Given θ be the measure of angle and radius of circle
The area of a sector of a circle (see diagram)
[tex]A = \frac{theta}{360} \pi r^{2}[/tex]
Given the radius of circle 'r' = 7cm and given angle θ = 45°
The area of a sector of a circle
[tex]A = \frac{45}{360} \pi( 7)^{2}[/tex]
Use pi =3.14
[tex]A = \frac{45X 3.14( 7)^{2}}{360}[/tex]
A = 19.2325
Final answer:-
The area of a sector of a circle = 19.2325
A manager wants to determine the number of containers to use for incoming parts for a kanban system to be installed next month. The process will have a usage rate of 83 pieces per hour. Because the process is new, the manager has assigned an inefficiency factor of .18. Each container holds 53 pieces and it takes an average of 80 minutes to complete a cycle. How many containers should be used? (Round up your answer to the next whole number.) Number of containers As the system improves, will more or fewer containers be required? More Fewer
Answer:
2 containers should be used
As the system improves, neither more or fewer containers be required
Step-by-step explanation:
According to the given data we have the following:
D=83 pieces per hour.
T=80 minutes=1.33 hour
X=0.18
C=53
In order to calculate how many containers should be used we would have to use the following formula:
Number of containers=DT(1+X)
C
Number of containers=(83)(1.33)(1+0.18)
53
Number of containers=2.45=2
2 containers should be used.
As the system improves, neither more or fewer containers be required
Josh has a drawer full of unmatched socks. There are 3 purple socks, 2 blue socks, 6 black socks, 4 brown socks, 5 yellow socks. If he reaches in his drawer, what is the probability of him drawing out a purple sock?Immersive Reader (9 Points) 1/5 2/5 3/5 3/20
Answer:
3/20
Step-by-step explanation:
because there is only 3 purple socks out of 20 socks total
A new postsurgical treatment was compared with a standard treatment. Eight subjects received the new treatment, while eight others (the controls) received the standard treatment. The recovery times, in days, are given below.
New Treatment Standard
12 18
13 23
15 24
19 30
20 32
21 35
24 39
Can you conclude that the mean recovery time for those receiving the new treatment differs from the mean for those receiving the standard treatment.
Answer:
1323
Step-by-step explanation:
HELP ASAP PLEASE
What type of graph would have the title, "Daily Low Temperatures Last Week"?
a. stem-and-leaf plot
b. line graph
c. bar graph
d. line plot
Answer:
line graph
Step-by-step explanation:
A very joyous band of cows reproduces at a rate of 30% per year. Curiously, however, 20% of the cow population per year spontaneously turn into rhinoceroses. The rhinoceroses also reproduce at 30% per year. 20% of the rhinoceroses per year run off to join the circus. Aliens with bad aim beam up 6 rhinoceroses per year. (a) Write down a system C and R, reflecting the facts above. Note the system is non-homogeneous. (b) Find and classify the equilibrium of the system.
Answer:
See explaination
Step-by-step explanation:
Kindly check attachment for the step by step solution of the given problem.
A 95% confidence interval for the proportion of students achieving a reading achievement score that is above the standard set by the teachers for a population of third grade students is (0.43, 0.49).
The margin of error of this interval is:
Group of answer choices
0.05
0.03
0.06
None of the above
The ratios in an equivalent ratio table are 3:12, 4:16, and 5:20. If the first number in the ratio is 10, what is the second number?
Answer:
The second number is 40
Step-by-Step:
There is a pattern in the ratio table: you need to multiply the first number by 4, and the answer is the second number. So if the first number is 10, you will need to multiply that by 4 to get the second number. So the second number is 40
A probability experiment is conducted in which the sample space of the experiment is
Upper S equals StartSet 7 comma 8 comma 9 comma 10 comma 11 comma 12 comma 13 comma 14 comma 15 comma 16 comma 17 comma 18 EndSetS={7,8,9,10,11,12,13,14,15,16,17,18}.
Let event
Upper E equals StartSet 7 comma 8 comma 9 comma 10 comma 11 comma 12 EndSetE={7,8,9,10,11,12}.
Assume each outcome is equally likely. List the outcomes in
Upper E Superscript cEc.
Find
?P(Upper E Superscript cEc?).
The outcomes in
Upper E Superscript cEc
are
StartSet nothing EndSet{}.
?(Use a comma to separate answers as? needed.)
?P(Upper E Superscript cEc?)equals=nothing
?(Type an integer or a simplified? fraction.)
Answer:
a) Eᶜ = {13,14,15,16,17,18}
The outcomes in Upper E Superscript c equals StartSet 13 comma 14 comma 15 comma 16 comma 17 comma 18 EndSet
b) P(Eᶜ) = (1/2) = 0.5
P(Upper E Superscript c) = (1/2) equals 0.5
Step-by-step explanation:
The set that represents the universal set with all the sample spaces is set S and is given by
Upper S equals StartSet 7 comma 8 comma 9 comma 10 comma 11 comma 12 comma 13 comma 14 comma 15 comma 16 comma 17 comma 18 EndSet
S = {7,8,9,10,11,12,13,14,15,16,17,18}
Upper E equals StartSet 7 comma 8 comma 9 comma 10 comma 11 comma 12 EndSet
Event E = {7,8,9,10,11,12}
a) Find Eᶜ
Eᶜ is the complement of event E; it includes all the outcomes in the universal set, S, that are not in the event E
Eᶜ = {13,14,15,16,17,18}
The outcomes in Upper E Superscript c equals StartSet 13 comma 14 comma 15 comma 16 comma 17 comma 18 EndSet
b) P(Upper E Superscript c) = P(Eᶜ)
= n(Eᶜ) ÷ n(S)
Each outcome is equally likely, hence,
n(Eᶜ) = number of outcomes in the event Eᶜ = 6
n(S) = number of outcomes in the set S = 12
P(Eᶜ) = (6/12) = (1/2) = 0.5
Hope this Helps!!!
Suppose that $4000 is deposited at 2% compounded quarterly. How much money will be in the account at the end of 6 years?
Answer:
$4,508.64
Step-by-step explanation:
The compound interest formula can answer this for you.
A = P(1 +r/n)^(nt)
where A is the account balance, P is the principal invested (4000), r is the annual interest rate (.02), n is the number of times per year interest is compounded (4), and t is the number of years (6).
Putting the given values into the formula, doing the arithmetic tells us ...
A = $4000(1 +.02/4)^(4·6) = $4000·1.005^24 ≈ $4,508.64
There will be $4,508.64 in the account at the end of 6 years.
Let X denote the voltage at the output of a microphone, and suppose that X has a uniform distribution on the interval from −1 to 1. The voltage is processed by a "hard limiter" with cutoff values −0.5 and 0.5, so the limiter output is a random variable Y related to X by Y = X if |X| ≤ 0.5, Y = 0.5 if X > 0.5, and Y = −0.5 if X < −0.5.
Answer:
Step-by-step explanation:
Please kindly go through the attached file for a step by step approach to the question.
The question discusses a scenario where the voltage output of a microphone, denoted by X, has a uniform distribution from -1 to 1. A hard limiter is applied which limits the output of X (denoted as Y) between -0.5 and 0.5, regardless of X's value.
Explanation:We have been given that X is a uniform distribution from -1 to 1. This essentially means that each value between -1 and 1 has an equal probability of occurring. A 'hard limiter' is applied with cutoff values of -0.5 and 0.5. Hence, the output Y is related to X as follows:
Y = X if |X| ≤ 0.5Y = 0.5 if X > 0.5Y = -0.5 if X < -0.5
This indicates that any voltage output greater than 0.5 or less than -0.5 will be limited, leading Y to fluctuate only between -0.5 and 0.5, irrespective of the value of X. Thus, the 'hard limiter' acts as a sort of boundary for the voltage output.
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Given a polynomial f(x), if (x + 2) is a factor, what else must be true? f(0) = 2 f(0) = −2 f(2) = 0 f(−2) = 0
Answer:
f(-2) = 0
Step-by-step explanation:
If x + 2 is a factor, then f(x) = 0 when x + 2 = 0.
x + 2 = 0
x = -2
f(-2) = 0
For the polynomial, f(0) = 2 and f(-2) = 0.
What is a polynomial?An expression that consists of variables, constants, and exponents that is combined using mathematical operations like addition, subtraction, multiplication, and division is referred to as a polynomial.
Given x+2 is a factor,
And values of x from the options are x = 0, -2 and 2.
We will put the values of x to the factor,
f(0) = 0 +2 = 2
f(-2) = -2 +2 = 0
f(2) = 4
Therefore from the result only two options satisfy the factor and those are f(0) = 2 and f(-2) = 0.
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What is the vertex of the graph of the function f(x) = 2(x − 2)2 + 3? Enter your answer in the boxes.
Answer:
The vertex of the function is at (2,3).
Step-by-step explanation:
I graphed the equation on the graph below.
If this answer is correct, please make me Brainliest!
The vertex of the graph of the function [tex]f(x)=2(x-2)^2+3[/tex] is at (2, 3). This is obtained by comparing the given function of the graph with the vertex form function of a parabola.
What is the vertex of a parabola?The vertex of a parabola is the point of intersection of the parabola and its line of symmetry.For a parabola whose equation is given in the standard form [tex]y=ax^2+bx+c[/tex], then the vertex will be the minimum of the graph if a>o and the maximum of the graph if a<0.The vertex form of a parabola is [tex]y=a(x-h)^2+k[/tex]. Where (h, k) is said to be the vertex of the graph.Finding the vertex:Given that the function of the graph is [tex]f(x)=2(x-2)^2+3[/tex].
We have the vertex form as [tex]y=a(x-h)^2+k[/tex]
So, the graph shows a parabola for the given equation.
On comparing the given equation with the vertex form,
f(x)=y, a=2, h=2, and k=3.
Then, (h, k)=(2, 3)
It is shown in the graph below.
Therefore, the vertex of the graph is at the point (2, 3).
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Item 6
Simplify the expression.
p^5⋅p^2
Answer:
p^7
Step-by-step explanation:
p^5⋅p^2 = p ^(5+2) = p^7
what two numbers have the sum of 2 and product of -48
Answer:
-6 and +8
Step-by-step explanation:
Hi there,
The best way to think about these is the fact that the sum is very small, but the product is big. So, these numbers must:
1. have a large absolute difference, since their sum is so small
2. the numbers are relatively close to each other in magnitude. Otherwise, you wouldn't get such a big product.
-6 * 8 = -48
-6 + 8 = +2
This makes sense, because they have a large absolute difference of 14 (8+6). Also, as absolute value +6 and +8 are pretty close to each other.
Keep practicing and have fun.
Marcela took out a $600 discount loan with a 4% annual interest rate over a period of 8 months. How much money does marcela get from the bank when she receives the loan? Round to the nearest dollar.
Answer:
Step-by-step explanation:
4 % of 600 over 8 months is 16
600-16=584
WILL GIVE BRAINLIEST!!!!!
IF 2 PEOPLE ANSWER!
An obtuse triangle is sometimes an example of a/an:
I.
scalene triangle
II.
isosceles triangle
III.
equilateral triangle
IV.
right triangle
Answer:
I.
Scalene triangle
Step-by-step explanation:
According to the Bureau of Labor Statistics it takes an average of 22 weeks for someone over 55 to find a new job. Assume that the probability distribution is normal and that the standard deviation is two weeks. What is the probability that eight workers over the age of 55 take an average of more than 20 weeks to find a job
Answer:
The probability that eight workers over the age of 55 will take an average of more than 20 weeks to find a job is 0.9977 or 99.77%
Step-by-step explanation:
Average time to find a new job for someone over 55 years = μ = 22 weeks
Standard deviation = σ = 2 weeks
We have to find the probability that if 8 workers are selected at random what will be the probability that it will take them more than 20 weeks to find a job. So, this means that the sample size is n = 8.
Since, the distribution is normal and we have the value of population standard deviation, we will use the z-distribution to find the desired probability. For this, first we need to convert the value (20 weeks) to its equivalent z-score. The formula to calculate the z-score is:
[tex]z=\frac{x-\mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
x = 20, converted to z-score will be:
[tex]z=\frac{20-22}{\frac{2}{\sqrt{8}}}=-2.83[/tex]
Thus, probability of time being greater than 20 weeks is equivalent to probability of z score being greater than - 2.83.
i.e.
P( X > 20 ) = P( z > -2.83 )
Using the z-table we can find this probability:
P( z > -2.83 ) = 1 - P( z < -2.83)
= 1 - 0.0023
= 0.9977
Since, P( X > 20 ) = P( z > -2.83 ), we can conclude that:
The probability that eight workers over the age of 55 will take an average of more than 20 weeks to find a job is 0.9977 or 99.77%
The probability that eight workers over the age of 55 take an average of more than 20 weeks to find a job is approximately 99.77%.
To solve this problem, we need to use the concepts of the sampling distribution of the sample mean and the properties of the normal distribution. Here are the steps to find the probability that the average time for eight workers over the age of 55 to find a job is more than 20 weeks:
Step 1: Understand the given data
- Mean time[tex](\(\mu\))[/tex] = 22 weeks
- Standard deviation [tex](\(\sigma\))[/tex] = 2 weeks
- Sample size [tex](\(n\))[/tex] = 8 workers
Step 2: Define the sampling distribution of the sample meanThe sample mean [tex]\(\bar{X}\)[/tex] for a sample of size (n) from a normal distribution with mean [tex]\(\mu\)[/tex] and standard deviation [tex]\(\sigma\)[/tex] is itself normally distributed with:
- Mean:[tex]\(\mu_{\bar{X}} = \mu\)[/tex]
- Standard deviation: [tex]\(\sigma_{\bar{X}} = \frac{\sigma}{\sqrt{n}}\)[/tex]
Calculate the standard deviation of the sample mean:
[tex]\[\sigma_{\bar{X}} = \frac{\sigma}{\sqrt{n}} = \frac{2}{\sqrt{8}} = \frac{2}{2.828} \approx 0.707\][/tex]
Step 3: Convert the problem to a standard normal distribution (Z)We want to find the probability that the sample mean [tex]\(\bar{X}\)[/tex] is greater than 20 weeks. First, we convert this to a Z-score:
[tex]\[Z = \frac{\bar{X} - \mu_{\bar{X}}}{\sigma_{\bar{X}}}\][/tex]
Calculate the Z-score for [tex]\(\bar{X} = 20\)[/tex] weeks:
[tex]\[Z = \frac{20 - 22}{0.707} = \frac{-2}{0.707} \approx -2.83\][/tex]
Step 4: Find the probability corresponding to the Z-scoreUsing standard normal distribution tables or a Z-score calculator, we find the probability that (Z) is less than -2.83.
The cumulative probability for (Z = -2.83) is approximately 0.0023. This represents the probability that the sample mean is less than 20 weeks. However, we want the probability that the sample mean is more than 20 weeks:
[tex]\[P(\bar{X} > 20) = 1 - P(\bar{X} \leq 20) = 1 - 0.0023 = 0.9977\][/tex]
Step 5: ConclusionThe probability that eight workers over the age of 55 take an average of more than 20 weeks to find a job is approximately 0.9977, or 99.77%.
Therefore, we can conclude that there is a very high probability (99.77%) that the average time for these eight workers to find a job is more than 20 weeks.
When Aubree goes bowling, her scores are normally distributed with a mean of 190 and a standard deviation of 14. Using the empirical rule, what percentage of the games that Aubree bowls does she score between 148 and 232?
Answer:
By the Empirical Rule, in 99.7% of the games that Aubree bowls she scores between 148 and 232
Step-by-step explanation:
The Empirical Rule states that, for a normally distributed random variable:
68% of the measures are within 1 standard deviation of the mean.
95% of the measures are within 2 standard deviation of the mean.
99.7% of the measures are within 3 standard deviations of the mean.
In this problem, we have that:
Mean = 190
Standard deviation = 14
Using the empirical rule, what percentage of the games that Aubree bowls does she score between 148 and 232?
148 = 190 - 3*14
So 148 is 3 standard deviations below the mean.
232 = 190 + 3*14
So 232 is 3 standard deviations above the mean
By the Empirical Rule, in 99.7% of the games that Aubree bowls she scores between 148 and 232